m 



MR. C. J. HARGREAVE ON THE CALCULATION OF ATTRACTIONS, 



The first part of this gives 4 «■ ^ 



tion between the surface and that spheroid on which the point lies, whose ellipticity is gj. 

 The (w + l)th term of V now becomes 



-(a9,a-9.a-^a2^a~^(^2__L)^2^a) 



a being semiaxis major of the stratum on which r lies. To determine the other part, 

 it is necessary to compute it when n = and w = 2, which gives 



To the sum of these we must add the value of V for the inner spheroid ; and for this 

 purpose we have to obtain V for an external point. 

 To the expression in (13.) we must add 



to be calculated when n = I and » = 3. This is .• 



The whole value of V is 



47r 



>. 



+ T- 



i^'-T 



P Fa' .a'* da' 



*/ 



After writing a for a, and s^ for s, add this to the other value of V, and apply the equa- 

 tions 



J'^" Fa' .a' da' — f^ ci'^ z' dp a! =• a^z(p a — d?z^(pdi— f^p d d (a'2 g'), 



-f^Fd ,d'^dd=.\J^' dUd<pd:=^2.U,p^^\£<pd!d{dU\ - 

 and similar equations for the other integrals ; and we shall obtain 



^?'/«-'P.«^-a9^a+<p,a + ^- \\^f^\dd{dH) -\-^f^%dd{d^^)^ 



V=:4crf 



